Methods and apparatus devised to determine particle size distributions by photosedimentation have been known for a long time. With them, the settling velocity (rate) of the particles suspended in the transparent liquid is the measure of the particle size. Sedimentation, in principle, can be effected in the gravitational field or in the centrifugal field. The attenuation of a light beam through the suspension is the measure of quantity, i.e. the amount of particles in a size fraction or class.
Two different sedimentation procedures are currently applied. In the case of the superimposed layer technique (line start technique) at the beginning of the analysis a layer of a concentrated suspension is superimposed over a body of clear liquid. In the case of the suspension technique the suspension is mixed uniformly at the start of the analysis.
With the suspension technique, having made transmission measurements T(t) in a photocentrifuge in response to the settling time (t), the particle size distribution q.sub.3 (x) can be calculated by numerical solution of the integral equation ##EQU1## wherein K(.pi.x/.lambda.) is the extinction function dependent on the material,
.rho..sub.f is the density of the suspension liquid, PA1 .eta. is the viscosity of the suspension liquid, PA1 .rho..sub.s is the density of the solids particles, PA1 c is a constant, PA1 .omega. is the number of revolutions of the centrifuge per unit of time, PA1 r is the inner radius of the cuvette, PA1 R is the radius at which the transmission measurement is made. PA1 .rho..sub.f is the density of the suspension liquid, PA1 .eta. is the viscosity of the suspension liquid, PA1 .rho..sub.s is the density of the solids particles, PA1 c is a constant, PA1 .omega. is the number of revolutions of the centrifuge per time unit, PA1 r is the inner radius of the cuvette, PA1 R is the radius at which the transmission measurement is made. PA1 q.sub.3 (x) from K(.alpha.) and .PHI.(.lambda..sub.i,x)=K(.pi.x/.lambda..sub.i) q.sub.3 (x).
The extinction function K must be known in order to be able to calculate the particle size distribution q.sub.3 (x). It belongs to the state of the art to either assume the extinction function K to be constant, or to calculate the extinction function according to the Mie theory. The first choice results in great errors when particles are small as against the light wavelength. The second possibility exists only with spherical particles of which the optical data of the material are known, which is not so in most cases. Only rarely are spherical particles given.
A method is known for photosedimentation under gravitation where the particles travel along straight, parallel paths. It is referred to as spectral photosedimentation with which the extinction function can be determined experimentally during the analysis. To that end, the analysis must be undertaken with light of different wavelengths (R. Weichert, Preprints of papers to be presented at the Fourth Particle Size Analysis Conference, Loughborough University of Technology, England, 21-24 Sep. 1981, pages 28 to 35).
The method of spectral photosedimentation analysis so far could not be applied in a centrifugal field because the particles are not moving along parallel paths, a condition for the spectral photosedimentation in the gravitational field.